- #1
e-pie
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- Homework Statement
- If $$A_i$$ is a covariant vector such that $$A_{i,j}+A_{j,i}=0$$, show that $$A_{i,jk}=-A_rR^r_{kij}$$ where $$R^r_{kij}$$ is the Riemann curvature tensor.
- Relevant Equations
- See below.
I derived this equation $$
A_{i,jk}-A_{i,kj}=R^r _{kij}A_r$$.But where do I use this $$A_{i,j}+A_{j,i}=0$$?
A_{i,jk}-A_{i,kj}=R^r _{kij}A_r$$.But where do I use this $$A_{i,j}+A_{j,i}=0$$?